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arXiv · 2607.26213

Astroid Spinodal Boundary in Phase-Based Ising Machines

Malihe Farasat·Nikhil Shukla
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Abstract

Oscillator Ising machines (OIMs) and dynamical Ising machines (DIMs) encode binary spins in phase states stabilized by second-harmonic injection (SHI). In a coupled network, the competition between SHI and the instantaneous local network field reshapes each oscillator's conditional energy landscape. We show that this competition drives a transition between monostable and bistable regimes through an astroid spinodal boundary. Near this boundary, the barrier scales as $\Delta E_i\propto\mu_i^{3/2}$ at generic smooth points and as $\Delta E_i\propto\mu_i^{2}$ at the longitudinal cusp. OIMs and DIMs obey the same spinodal geometry, with their conditional landscapes related by a reversal of the transverse field. Finally, the first-harmonic conditional landscape is mathematically equivalent, up to an additive constant, to the Stoner--Wohlfarth energy of a uniaxial magnetic particle.

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Malihe Farasat, Nikhil Shukla. 2026-07-28. Astroid Spinodal Boundary in Phase-Based Ising Machines. https://arxiv.org/abs/2607.26213

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